Question

In the laboratory the life time' of a particle moving with speed 2.8x108m/s, is found to be 2.5x10-7 sec. Calculate the proper life time of the particle.

Answer 1

Answer:We have to multiply the observed lifetime of the particle by (1-v exp 2/c exp 2) where v is the speed of the particle and c the velocity of light in vacuum. Proper lifetime will be less than the observed lifetime.

Explanation:

Answer 2

The proper life time of the particle is $8.97\times10^{-8}\ sec$

Explanation:

Given that,

Speed of particle $v=2.8\times10^{8}\ m/s$

Time $t= 2.5\times10^{-7}\ sec$

We need to calculate the proper life time of the particle

Using formula of proper time

$t'=\dfrac{t_{0}}{\sqrt{1-(\dfrac{v}{c})^2}}$

Where, v = speed of the particle

c = speed of light

t' = observer time

Put the value into the formula

$2.5\times10^{-7}=\dfrac{t_{0}}{\sqrt{1-(\dfrac{2.8\times10^{8}}{3\times10^{8}})^2}}$

$t_{0}=2.5\times10^{-7}\times\sqrt{1-(\dfrac{2.8\times10^{8}}{3\times10^{8}})^2}$

$t_{0}=8.97\times10^{-8}\ sec$

Hence, The proper life time of the particle is $8.97\times10^{-8}\ sec$

learn more :

Topic : proper time

https://brainly.in/question/5569462